Problem: Solve for $x$ : $3x^2 + 39x + 108 = 0$
Solution: Dividing both sides by $3$ gives: $ x^2 + {13}x + {36} = 0 $ The coefficient on the $x$ term is $13$ and the constant term is $36$ , so we need to find two numbers that add up to $13$ and multiply to $36$ The two numbers $9$ and $4$ satisfy both conditions: $ {9} + {4} = {13} $ $ {9} \times {4} = {36} $ $(x + {9}) (x + {4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x + 4) = 0$ $x + 9 = 0$ or $x + 4 = 0$ Thus, $x = -9$ and $x = -4$ are the solutions.